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Bài 9,
62x73+36x33=36x73+36x27=36(73+27)=36x100=3600.
197-\([\)6x(5-1)2+20220\(]\):5=197-\([\)6x16+1\(]\):5=197-97:5=197-97/5=888/5.
Bài 10,
21-4x=13
=>4x=21-13=8
=>x=8:4=2.
30:(x-3)+1=45:43=42=16
=>30:(x-3)=16-1=15
=>x-3=30:15=2
=>x=2+3=5.
(x-1)3+5x6=38
=>(x-1)3+30=38
=>(x-1)3=38-30=8=23
=>x-1=2
=>x=3.
+) \(x^3=x^2\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
+) \((7x-11)^3=2^5.5^2+200\)
\((7x-11)^3=2^3.2^2.5^2+2^3.5^2\)
\((7x-11)^3=2^3.5^2.(2^2+1)\)
\((7x-11)^3=2^3.5^2.5\)
\((7x-11)^3=2^3.5^3\)
\((7x-11)^3=10^3\)
\(\Rightarrow7x-11=10\)
\(7x=21\)
\(x=3\)
+) \(3+2^{x-1}=24-[4^2-(2^2-1)]\)
\(3+2^{x-1}=11\)
\(2^{x-1}=8\)
\(2^{x-1}=2^3\)
\(\Rightarrow x-1=3\)
\(x=4\)
a) \(5\left(x+7\right)-10=2^3\cdot5\)
\(\Rightarrow5\left(x+7\right)-10=40\)
\(\Rightarrow5\left(x+7\right)=40+10\)
\(\Rightarrow x+7=\dfrac{50}{5}\)
\(\Rightarrow x+7=10\)
\(\Rightarrow x=10-7\)
\(\Rightarrow x=3\)
b) \(9x-2\cdot3^2=3^4\)
\(\Rightarrow9x-18=81\)
\(\Rightarrow9x=81+18\)
\(\Rightarrow9x=99\)
\(\Rightarrow x=\dfrac{99}{9}\)
\(\Rightarrow x=11\)
c) \(5^{25}\cdot5^{x-1}=5^{25}\)
\(\Rightarrow5^{x-1}=5^{25}:5^{25}\)
\(\Rightarrow5^{x-1}=1\)
\(\Rightarrow5^{x-1}=5^0\)
\(\Rightarrow x-1=0\)
\(\Rightarrow x=1\)
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Câu a mình ko bt trình bày thông cảm
b) \(^{2^x.\left(2^2\right)^2=\left(2^3\right)^2}\)
\(2^x.2^4=2^6\)
\(2^x=2^6:2^4\)
\(2^x=2^2\)
\(x=2\)
Lời giải:
$1+2+2^3+2^4+2^5+...+2^{x+1}=1023$
$2^3+2^4+2^5+...+2^{x+1}=1020(1)$
$2^4+2^5+2^6+...+2^{x+2}=2040(2)$
Lấy (2) trừ (1) theo vế suy ra:
$2^{x+2}-2^3=2040-1020=1020$
$2^{x+2}=1028$
Với giá trị này sẽ không tồn tại số tự nhiên x. Bạn xem lại đề.
a) x=3
b) x=1
c) x=1 hoặc -5
d) x=2
e) x=2
g) x=2
h) x=1 hoặc x=0 hoặc x=-1
i) x=-1 hoặc x=0
\(a.4^x=64\)
\(4^x=4^3\)
\(\Rightarrow x=3\)
\(b,3^{x\times4}=81\)
\(3^{x\times4}=3^4\)
\(x\times4=4\)
\(\Rightarrow x=1\)
\(c,\left(2+x\right)^4=81\)
\(\left(2+x\right)^4=3^4\)
\(2+x=3\)
\(x=3-2\)
\(x=1\)
\(d,5^{x\times5}=125\)
\(5^{x\times5}=5^3\)
\(x\times5=3\)
\(x=3:5\)
\(x=\frac{3}{5}\)
a: \(2^x=2^3\)
nên x=3
c: \(11^x=1331\)
nên x=3
d: \(2^x+4=12\)
nên \(2^x=8\)
hay x=3
a) \(5.3^x=405\)
\(\Rightarrow3^x=405:5\)
\(\Rightarrow3^x=81=3^4\)
\(\Rightarrow x=4\)
b) \(\left(x-2\right)^5=243\)
\(\Rightarrow\left(x-2\right)^5=3^5\)
\(\Rightarrow x-2=3\)
\(\Rightarrow x=5\)
c) \(2^x+2^{x+4}=272\)
\(\Rightarrow2^x.\left(1+2^4\right)=272\)
\(\Rightarrow2^x.17=272\)
\(\Rightarrow2^x=272:17=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
d) Từ x + 1 đến x + 2 có số số hạng là: (30 - 1) : 1 + 1 = 30 (số)
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=795\)
\(\Rightarrow30x+\frac{\left(30+1\right).30}{2}=795\)
\(\Rightarrow30x+465=795\)
\(\Rightarrow30x=330\)
\(\Rightarrow x=330:30\)
\(\Rightarrow x=11\)
a) \(5.3^x=405\)
\(3^x=\frac{405}{5}=81\)
\(3^x=3^4\)
Vậy x = 4
b ) \(\left(x-2\right)^5=243\)
\(\left(x-2\right)^5=3^5\)
\(\Rightarrow x-2=3\)
\(\Rightarrow x=3+2=5\)
Vậy x = 5